A mass M attached to a horizontal spring exec | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) At the mean position,the velocity of the mass $M$ is maximum,given by $v_{max} = \omega_1 A_1 = \sqrt{\frac{k}{M}} A_1$. When mass $m$ is placed o

Vedclass · Accepted Answer

$\left(\frac{M+m}{M}\right)^{\frac{1}{2}}$

Vedclass · Answer

(C) At the mean position,the velocity of the mass $M$ is maximum,given by $v_{max} = \omega_1 A_1 = \sqrt{\frac{k}{M}} A_1$. When mass $m$ is placed on $M$,the total mass becomes $(M+m)$. Since the collision is perfectly inelastic and occurs at the mean position,the momentum is conserved. $M v_{max} = (M+m) v'_{max}$. So,$v'_{max} = \frac{M}{M+m} v_{max}$. The new angular frequency is $\omega_2 = \sqrt{\frac{k}{M+m}}$. Since $v'_{max} = \omega_2 A_2$,we have $\frac{M}{M+m} (\omega_1 A_1) = \omega_2 A_2$. Substituting the values: $\frac{M}{M+m} \sqrt{\frac{k}{M}} A_1 = \sqrt{\frac{k}{M+m}} A_2$. $\frac{A_1}{A_2} = \frac{M+m}{M} \sqrt{\frac{k}{M+m}} \sqrt{\frac{M}{k}} = \frac{M+m}{M} \sqrt{\frac{M}{M+m}} = \sqrt{\frac{M+m}{M}} = \left(\frac{M+m}{M}\right)^{\frac{1}{2}}$.

$A$ mass $M$ attached to a horizontal spring executes $S.H.M.$ of amplitude $A_1$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio $\left(\frac{A_1}{A_2}\right)$ is

Similar Questions

The value of $\lambda$ with $|\lambda| < 16$ such that $2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0$ represents a pair of straight lines,is

If the slope of one of the lines given by $ax^2+2hxy+by^2=0$ is two times the other,then:

For all integers $n \geq 1$, which of the following is divisible by $9$?

In a first order reaction,the concentration of the reactant decreases from $0.6 \ M$ to $0.3 \ M$ in $15 \ min$. The time taken for the concentration to change from $0.1 \ M$ to $0.025 \ M$ in minutes is

In which reaction is a racemic mixture not obtained?

Vedclass Test Series

Exam Paper Generator

Online Exam Module